?'(x) convolved with G(x)

/tuning-math/files/MikeBattaglia/%3F%28x%29%20convolved%20with%20g%28x%29/

Gene sent me this offlist, so I gave it a shot. It ends up looking
like HE if you seed things with the Stern-Brocot tree.

Four options there. The fact that at the far ends of the graph things
jump all over the place is because of artifacts that occur because
there is no data before the endpoints to do the convolution with. I
didn't realize until afterward that a solution existed for this with
?(x), I missed it in Gene's original email to me offlist. I just spent
a lot of time on this and will have to come back to it though - you
can get a glimpse of what it'll look like once I get the endpoint
solution fixed.

Not sure how to work out a solution with ?(2^x), but I'm sure MATLAB
has a way to interpolate from one function to another. I have to
figure out how though.

-Mike